/*
自己选择的路 ,跪着也要走完。朋友们 , 虽然这个世界日益浮躁起来,只
要能够为了当时纯粹的梦想和感动坚持努力下去 , 不管其它人怎么样,我
们也能够保持自己的本色走下去。
To the world , you will be a person , but to a person , you
will be the world .                               ——AKPower
*/
//作者:AKPower
//算法:
#include <iostream>
#include <cmath>
#include <algorithm>
#include <cstring>
#include <vector>
#include <map>
#include <queue>
#include <cstdio>
#include <string>
#include <stack>
#include <set>
#define IOS ios::sync_with_stdio(false), cin.tie(0)
using namespace std;
typedef long long ll;
const ll maxn = 1e5 + 100;
ll a[maxn];
ll n, k, t;
int main()
{
    IOS;
    cin >> t;
    while (t--)
    {
        cin >> n >> k;
        ll max_a = -1, id = 0, pre = 0;
        for (ll i = 1; i <= n; i++)
        {
            cin >> a[i];
            pre += a[i];
            if (a[i] > max_a)
            {
                max_a = a[i];
                id = i;
            }
        }
        ll div1 = max_a + n - 1;
        ll div2 = pre;
        pre = 0;
        for (ll i = 1; i < id; i++)
        {
            pre += a[i];
        }
        if (k >= id - 1 && k <= pre)
        {
            cout << "YES" << endl;
            continue;
        }
        if (k < id - 1)
        {
            cout << "NO" << endl;
            continue;
        }
        ll sh1 = k - pre;
        ll sh2 = k - (id - 1);
        if (sh2 < div1)
        {
            cout << "NO" << endl;
            continue;
        }
        if (sh1 > div2)
        {
            if (sh2 - sh1 >= div2 - div1)
            {
                cout << "YES" << endl;
            }
            else
                cout << "NO" << endl;
            continue;
        }
        cout << "YES" << endl;
    }
    getchar();
    getchar();
    return 0;
}
